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Perfect computational equivalence between quantum turing machines and finitely generated uniform quantum circuit families (2008)
| Citations: | 4 - 0 self |
BibTeX
@TECHREPORT{Nishimura08perfectcomputational,
author = {Harumichi Nishimura and Masanao Ozawa},
title = {Perfect computational equivalence between quantum turing machines and finitely generated uniform quantum circuit families},
institution = {},
year = {2008}
}
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Abstract
In order to establish the computational equivalence between quantum Turing machines (QTMs) and quantum circuit families (QCFs) using Yao’s quantum circuit simulation of QTMs, we previously introduced the class of uniform QCFs based on an infinite set of elementary gates, which has been shown to be computationally equivalent to the polynomial-time QTMs (with appropriate restriction of amplitudes) up to bounded error simulation. This result implies that the complexity class BQP introduced by Bernstein and Vazirani for QTMs equals its counterpart for uniform QCFs. However, the complexity classes ZQP and EQP for QTMs do not appear to equal their counterparts for uniform QCFs. In this paper, we introduce a subclass of uniform QCFs, the finitely generated uniform QCFs, based on finite number of elementary gates and show that the class of finitely generated uniform QCFs is perfectly equivalent to the class of polynomial-time QTMs; they can exactly simulate each other. This naturally implies that BQP as well as ZQP and EQP equal the corresponding complexity classes of the finitely generated uniform QCFs. 1
Keyphrases
uniform qcfs perfect computational equivalence uniform quantum circuit family polynomial-time qtms elementary gate generated uniform qcfs complexity class bqp computational equivalence appropriate restriction circuit family quantum turing machine corresponding complexity class yao quantum circuit simulation error simulation infinite set finite number
